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In a way, he did. Star Trek helped to break the racial barriers of 1960's America, and inspired a generation of scientists and engineers to invent things that we use commonly today.

There was an entire generation of people who saw what Star Trek brought to the TV screen, and wanted to bring it into reality. Gene saw thousands of fans were inspired to become a better person because of an idea he had one day.

People saw an interracial kiss on screen for the first time. Some were outraged, most didn't see a problem. Some saw a Japanese person working equally with white crewmen while Japanese-Americans still were treated like garbage and had their possessions still stripped from them.

Roddenberry intended the show to have a progressive political agenda reflective of the emerging counter-culture of the youth movement, though he was not fully forthcoming to the networks about this. He wanted Star Trek to show what humanity might develop into, if it would learn from the lessons of the past, most specifically by ending violence. An extreme example is the alien species known as the Vulcans, who had a violent past but learned to control their emotions. Roddenberry also gave Star Trek an anti-war message and depicted the United Federation of Planets as an ideal, optimistic version of the United Nations.[15] His efforts were opposed by the network because of concerns over marketability, e.g., they opposed Roddenberry's insistence that Enterprise have a racially diverse crew.[16]

Gene didn't live to see a post-scarcity, no violence, bigotry free society, but he inspired people to achieve it. Gene died happy with knowing he sparked an entire idea into action, some day in the future.